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An Introduction to Particle Accelerators

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Title: An Introduction to Particle Accelerators


1
An Introduction to Particle Accelerators
  • Erik Adli, University of Oslo/CERN
  • 2009
  • Erik.Adli_at_cern.ch

v1.42 - short
2
LHC FIRST BEAM 10-sep-2008
3
Introduction
Part 1
4
Particle accelerators for HEP
  • LHC the world biggest accelerator, both in
    energy and size (as big as LEP)
  • Grand start-up and perfect functioning at
    injection energy in September 2008
  • First collisions expected in 2009

5
Particle accelerators for HEP
The next big thing. After LHC, a Linear Collider
of over 30 km length, will probably be needed
(why?)
6
Medical applications
  • Therapy
  • The last decades electron accelerators
    (converted to X-ray via a target) are used very
    successfully for cancer therapy)
  • Today's research proton accelerators instead
    (hadron therapy) energy deposition can be
    controlled better, but huge technical challenges
  • Imaging
  • Isotope production for PET scanners

7
Advantages of proton / ion-therapy
( Slide borrowed from U. Amaldi )
8
Proton therapy accelerator centre
HIBAC in Chiba
What is all this? Follow the lectures... )
( Slide borrowed from U. Amaldi )
9
Synchrotron Light Sources
  • the last two decades, enormous increase in the
    use of synchrony radiation, emitted from particle
    accelerators
  • Can produce very intense light (radiation), at a
    wide range of frequencies (visible or not)
  • Useful in a wide range of scientific applications

10
Thorium - Accelerator Driven Systems
11
Basic concepts
Part 2
12
An accelerator
  • Structures in which the particles will move
  • Structures to accelerate the particles
  • Structures to steer the particles

13
Lorentz equation
  • The two main tasks of an accelerator
  • Increase the particle energy
  • Change the particle direction (follow a given
    trajectory, focusing)
  • Lorentz equation
  • FB ? v ? FB does no work on the particle
  • Only FE can increase the particle energy
  • FE or FB for deflection? v ? c ? Magnetic field
    of 1 T (feasible) same bending power as en
    electric field of 3?108 V/m (NOT feasible)
  • FB is by far the most effective in order to
    change the particle direction

14
Acceleration techniques DC field
  • The simplest acceleration method DC voltage
  • Energy kick DEqV
  • Can accelerate particles over many gaps
    electrostatic accelerator
  • Problem breakdown voltage at 10MV
  • DC field still used at start of injector chain

15
Acceleration techniques RF field
  • Oscillating RF (radio-frequency) field
  • Widerøe accelerator, after the pioneering work
    of the Norwegian Rolf Widerøe (brother of the
    aviator Viggo Widerøe)
  • Particle must sees the field only when the field
    is in the accelerating direction
  • Requires the synchronism condition to hold
    Tparticle ½TRF
  • Problem high power loss due to radiation

16
Acceleration techniques RF cavities
  • Electromagnetic power is stored in a resonant
    volume instead of being radiated
  • RF power feed into cavity, originating from RF
    power generators, like Klystrons
  • RF power oscillating (from magnetic to electric
    energy), at the desired frequency
  • RF cavities requires bunched beams (as opposed to
    coasting beams)
  • particles located in bunches separated in space

17
From pill-box to real cavities
(from A. Chao)
LHC cavity module
ILC cavity
18
Why circular accelerators?
  • Technological limit on the electrical field in an
    RF cavity (breakdown)
  • Gives a limited ?E per distance
  • ? Circular accelerators, in order to re-use the
    same RF cavity
  • This requires a bending field FB in order to
    follow a circular trajectory (later slide)

19
The synchrotron
  • Acceleration is performed by RF cavities
  • (Piecewise) circular motion is ensured by a guide
    field FB
  • FB Bending magnets with a homogenous field
  • In the arc section
  • RF frequency must stay locked to the revolution
    frequency of a particle (later slide)
  • Synchrotrons are used for most HEP experiments
    (LHC, Tevatron, HERA, LEP, SPS, PS) as well as,
    as the name tells, in Synchrotron Light Sources
    (e.g. ESRF)

20
Digression other accelerator types
  • Cyclotron
  • constant B field
  • constant RF field in the gap increases energy
  • radius increases proportionally to energy
  • limit relativistic energy, RF phase out of synch
  • In some respects simpler than the synchrotron,
  • and often used as medical accelerators
  • Synchro-cyclotron
  • Cyclotron with varying RF phase
  • Betatron
  • Acceleration induced by time-varying magnetic
    field
  • The synchrotron will be the only circular
    accelerator discussed in this course

21
Digression other accelerator types
  • Linear accelerators for linear colliders
  • - will be covered in lecture about linear
    colliders at CERN

22
Particle motion
  • We separate the particle motion into
  • longitudinal motion motion tangential to the
    reference trajectory along the accelerator
    structure, us
  • transverse motion degrees of freedom orthogonal
    to the reference trajectory, ux, uy
  • us, ux, uy are unit vector in a moving coordinate
    system, following the particle

23
Longitudinal dynamicsfor a synchrotron
Part 3
Longitudinal Dynamics degrees of freedom
tangential to the reference trajectory us
tangential to the reference trajectory
24
RF acceleration
  • We assume a cavity with an oscillating RF-field
  • In this section we neglect the transit-transit
    factor
  • we assume a field constant in time while the
    particle passes the cavity
  • Work done on a particle inside cavity

25
Synchrotron with one cavity
  • The energy kick of a particle, DE, depends on the
    RF phase seen, f
  • We define a synchronous particle, s, which
    always sees the same phase fs passing the cavity
  • ? wRF h wrs ( h harmonic number )
  • E.g. at constant speed, a synchronous particle
    circulating in the synchrotron, assuming no
    losses in accelerator, will always see fs0

26
Non-synchronous particles
  • A synchronous particle P1 sees a phase fs and get
    a energy kick DEs
  • A particle N1 arriving early with f fs-d will
    get a lower energy kick
  • A particle M1 arriving late with f fsd will get
    a higher energy kick
  • Remember in a synchrotron we have bunches with a
    huge number of particles, which will always have
    a certain energy spread!

27
Frequency dependence on energy
  • In order to see the effect of a too low/high DE,
    we need to study the relation between the change
    in energy and the change in the revolution
    frequency (h "slip factor")
  • Two effects
  • Higher energy ? higher speed (except
    ultra-relativistic)
  • Higher energy ? larger orbit Momentum
    compaction

28
Momentum compaction
  • Increase in energy/mass will lead to a larger
    orbit
  • We define the momentum compaction factor as
  • a is a function of the transverse focusing in
    the accelerator, altDxgt / R
  • ? a is a well defined quantity for a given
    accelerator

29
Phase stability
  • hgt0 velocity increase dominates, fr increases
  • Synchronous particle stable for 0ºltfslt90º
  • A particle N1 arriving early with f fs-d will
    get a lower energy kick, and arrive relatively
    later next pass
  • A particle M1 arriving late with f fsd will get
    a higher energy kick, and arrive relatively
    earlier next pass
  • hlt0 stability for 90ºltfslt180º
  • h0 at the transition energy. When the
    synchrotron reaches this energy, the RF phase
    needs to be switched rapidly from fs to 180-fs

30
Transverse dynamics
Part 4
Transverse dynamics degrees of freedom
orthogonal to the reference trajectory ux the
horizontal plane uy the vertical plane
31
Bending field
  • Circular accelerators deflecting forces are
    needed
  • Circular accelerators piecewise circular orbits
    with a defined bending radius ?
  • Straight sections are needed for e.g. particle
    detectors
  • In circular arc sections the magnetic field must
    provide the desired bending radius
  • For a constant particle energy we need a constant
    B field ? dipole magnets with homogenous field
  • In a synchrotron, the bending radius,1/?eB/p, is
    kept constant during acceleration (last section)

32
The reference trajectory
  • An accelerator is designed around a reference
    trajectory (also called design orbit in circular
    accelerators)
  • This is the trajectory an ideal particle will
    follow and consist of
  • a straight line where there is no bending field
  • arc of circle inside the bending field
  • We will in the following talk about transverse
    deviations from this reference trajectory, and
    especially about how to keep these deviations
    small

33
Bending field dipole magnets
  • Dipole magnets provide uniform field in the
    desired region
  • LHC Dipole magnets design that allows opposite
    and uniform field in both vacuum chambers
  • Bonus effect of dipole magnets geometrical
    focusing in the horizontal plane
  • 1/? normalized dipole strength, strength of
    the magnet

34
Focusing field
  • reference trajectory typically centre of the
    dipole magnets
  • Problem with geometrical focusing still large
    oscillations and NO focusing in the vertical
    plane ? the smallest disturbance (like
    gravity...) may lead to lost particle
  • Desired a restoring force of the type Fx,y-kx,y
    in order to keep the particles close to the ideal
    orbit
  • A linear field in both planes can be derived from
    the scalar pot. V(x,y) gxy
  • Equipotential lines at xyVconst
  • B ? magnet iron surface
  • ? Magnet surfaces shaped as hyperbolas gives
    linear field

35
Focusing field quadrupoles
  • Quadrupole magnets gives linear field in x and y
  • Bx -gy
  • By -gx
  • However, forces are focusing in one plane and
    defocusing in the orthogonal plane
  • Fx -qvgx (focusing)
  • Fy qvgy (defocusing)
  • Opposite focusing/defocusing is achieved by
    rotating the quadrupole 90?
  • Analogy to dipole strength normalized quadrupole
    strength

inevitable due to Maxwell
36
Optics analogy
  • Physical analogy quadrupoles ? optics
  • Focal length of a quadrupole 1/f kl
  • where l is the length of the quadrupole
  • Alternating focusing and defocusing lenses will
    together give total focusing effect in both
    planes (shown later)
  • Alternating Gradient focusing

37
The Lattice
  • An accelerator is composed of bending magnets,
    focusing magnets and non-linear magnets (later)
  • The ensemble of magnets in the accelerator
    constitutes the accelerator lattice

38
Example lattice components
39
Transverse beam size
  • RMS beam size

Lattice
Beam quality
40
Conclusion transverse dynamics
  • We have now studied the transverse optics of a
    circular accelerator and we have had a look at
    the optics elements,
  • the dipole for bending
  • the quadrupole for focusing
  • the sextupole for chromaticity correction
  • All optic elements ( more) are needed in a high
    performance accelerator, like the LHC

41
Synchrotron radiation
Part 5
42
1) Synchrotron radiation
  • Charged particles undergoing acceleration emit
    electromagnetic radiation
  • Main limitation for circular electron machines
  • RF power consumption becomes too high
  • The main limitation factor for LEP...
  • ...the main reason for building LHC !
  • However, synchrotron radiations is also useful
    (see later slides)

43
Show RAD2D here
  • (anim)

44
Characteristic of SR power
45
Characteristics of SR distribution
  • Electron rest-frame radiation distributed as a
    "Hertz-dipole"
  • Relativist electron Hertz-dipole distribution in
    the electron rest-frame, but transformed into the
    laboratory frame the radiation form a very
    sharply peaked light-cone

46
Characteristics of SR spectrum
  • Broad spectra (due to short pulses as seen by an
    observer)
  • But, 50 of power contained within a well defined
    "critical frequency"
  • Summary advantages of Synchrotron Radiation
  • Very high intensity
  • Spectrum that cannot be covered easy with other
    sources
  • Critical frequency easily controlled

47
Typical SR centre
Example European Synchrotron Radiation Facility
(ESRF), Grenoble, France
Accelerator Users
  • Some applications of Synchrotron Radiation
  • material/molecule analysis (UV, X-ray)
  • crystallography
  • archaeology...

48
Case LHC
49
LHC
50
LHC injector system
  • LHC is responsible for accelerating protons from
    450 GeV up to 7000 GeV
  • 450 GeV protons injected into LHC from the SPS
  • PS injects into the SPS
  • LINACS injects into the PS
  • The protons are generated by a Duoplasmatron
    Proton Source

51
LHC layout
  • circumference 26658.9 m
  • 8 interaction points, 4 of which contains
    detectors where the beams intersect
  • 8 straight sections, containing the IPs, around
    530 m long
  • 8 arcs with a regular lattice structure,
    containing 23 arc cells
  • Each arc cell has a FODO structure, 106.9 m long

52
LHC beam transverse size
beta in drift space b(s) b (s-s)2 / b
53
LHC cavities
  • Superconducting RF cavities (standing wave, 400
    MHz)
  • Each beam one cryostats with 44 cavities each
  • Located at LHC point 4

54
LHC main parametersat collision energy
55
References
  • Bibliography
  • K. Wille, The Physics of Particle Accelerators,
    2000
  • ...and the classic E. D. Courant and H. S.
    Snyder, "Theory of the Alternating-Gradient
    Synchrotron", 1957
  • CAS 1992, Fifth General Accelerator Physics
    Course, Proceedings, 7-18 September 1992
  • LHC Design Report online
  • Other references
  • USPAS resource site, A. Chao, USPAS january 2007
  • CAS 2005, Proceedings (in-print), J. Le Duff, B,
    Holzer et al.
  • O. Brüning CERN student summer lectures
  • N. Pichoff Transverse Beam Dynamics in
    Accelerators, JUAS January 2004
  • U. Amaldi, presentation on Hadron therapy at CERN
    2006
  • Several figures in this presentation have been
    borrowed from the above references, thanks to all!
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